First let me quote the N/A text again:
ἔτι γὰρ Χριστὸς ὄντων ἡμῶν ἀσθενῶν ἔτι κατὰ καιρὸν ὑπὲρ ἀσεβῶν ἀπέθανεν.
It will be helpful to look more into the different senses of ἔτι. Louw&Nida has three senses:
a still: 67.128
b in addition: 59.75
c nevertheless: 89.135
For each of these they give a bit more explanation:
67.128 ἀκμήν; ἔτι; τὸ λοιπόν: extension of time up to and beyond an expected point—‘still, yet.’ἀκμήν: ἀκμὴν καὶ ὑμεῖς ἀσύνετοί ἐστε; ‘are you still without understanding?’ Mt 15:16.
ἔτι: ἔτι αὐτοῦ λαλοῦντος ἰδοὺ Ἰούδας εἷς τῶν δώδεκα ἦλθεν ‘he was still speaking when Judas, one of the twelve, arrived’ Mt 26:47.
However, it is not always helpful to lump three different words together as if there was no difference in meaning, so I'd like to supplement with BDAG:
① pert. to continuance, yet, still (contrast ἤδη ‘already’–ἔτι ‘still’.)
ⓐ in positive statements, to denote that a given situation is continuing still, yet.
The word order indicates the prominence of the adverb as compared to the other elements in the sentence. When there is an element of unexpectedness or contrast, the word comes at the front. In order words, the more to the left the word is placed, the more relative prominence it has.
L&N: 59.75 ἔτι: the state of something being in addition to what already exists—‘in addition, besides.’
ⓑ that which is added to what is already at hand.
I would consider the first ἔτι in our verse to indicate an addition, or a continuation of the argumentation. It is not translated in English versions, but might be rendered: On top of that...
The second ἔτι belongs to the genitive absolute as a continuation of a state, but it is not in focus and is therefore placed last. Christ died for us when we were in a state of weakness, still. There is no focus on unexpectedness or contrast in this state as there is in Rom 5:8.
It is not so common to use ἔτι without a focus, so a placement at the end is not common. The placement is part of the intended meaning. We have a similar last placement in Rev 22.11 for the continuation of a state.:
ὁ ἀδικῶν ἀδικησάτω ἔτι, καὶ ὁ ῥυπαρὸς ῥυπανθήτω ἔτι, καὶ ὁ δίκαιος δικαιοσύνην ποιησάτω ἔτι καὶ ὁ ἅγιος ἁγιασθήτω ἔτι.
It was mentioned that the Byzantine text does not have the second ἔτι. I think this reflects that the word is not in focus and is, in fact, expendable. It adds very little to the meaning of the sentence.
In case someone is wondering, I have never bought into the topic-comment theory of lingusitics.